Question: What's the first wrong statement in the proof below that $ \triangle BCE \cong \triangle BCA$ $ \; ?$ $ \overline{BC} $ is parallel to $ \overline{DF} $. This diagram is not drawn to scale. $A$ $B$ $C$ $D$ $E$ $F$ Givens $ \angle BAC \cong \angle BED$ $, \ $ $ \overline{AC} \cong \overline{DE}$ $, \ $ $ \angle ACB \cong \angle BDE$ $, \ $ $ \overline{BC} \cong \overline{CF}$ $, \ $ $ \angle ABC \cong \angle CFE$ $, \ $ and $\ $ $ \overline{AB} \cong \overline{EF}$ Proof $ \triangle BDE \cong \triangle BCA$ because ASA $ \overline{BE} \cong \overline{AB}$ because corresponding parts of congruent triangles are congruent $ \triangle FCE \cong \triangle BCE$ because AAS $ \triangle BCA \cong \triangle FCE$ because SAS $ \angle BAC \cong \angle CEF$ because corresponding parts of congruent triangles are congruent $ \triangle BCE \cong \triangle BCA$ because SSS
Answer: Try going through the proof yourself: write down the givens, and then see if they justify the next step for the reason given. Then do the same thing for the next step, and the next, until you run into something that you can't justify, or you finish the proof. $ \triangle BCE \cong \triangle FCE$ is the first wrong statement.